A Splitting Method for Deep Water with Bathymetry

Abstract : In this paper we derive and prove the wellposedness of a deep water model that generalizes the Saut-Xu system for nonflat bottoms. Then, we present a new numerical method based on a splitting approach for studying this system. The advantage of this method is that it does not require any low pass filter to avoid spurious oscillations. We prove a local error estimate and we show that our scheme represents a good approximation of order one in time. Then, we perform some numerical experiments which confirm our theoretical result and we study three physical phenomena : the evolution of water waves over a rough bottom; the evolution of a KdV soliton when the shallowness parameter increases; the homogenization effect of rapidly varying topographies on water waves.
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https://hal.archives-ouvertes.fr/hal-01326794
Contributor : Benjamin Melinand <>
Submitted on : Tuesday, February 14, 2017 - 4:21:28 PM
Last modification on : Tuesday, April 17, 2018 - 9:04:53 AM

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  • HAL Id : hal-01326794, version 2
  • ARXIV : 1606.01630

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Afaf Bouharguane, Benjamin Melinand. A Splitting Method for Deep Water with Bathymetry. 2017. ⟨hal-01326794v2⟩

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